Since the early days of quantum mechanics entanglement has been considered one of the crucial and most interesting properties of quantum systems [1]}.
In the last two decades, a renewed interest in this subject has lead to many insights into various branches of physics, ranging from quantum gravity and holography to critical and topological many-body systems [2]}, [3]}, [4]}, [5]}, [6]}.
Quantifying the entanglement between a spatial region \(A\)  in a given system and its complement \(B\)  is particularly important. We assume that the Hilbert space \(\mathcal {H}\)  of the entire system factorizes as \(\mathcal {H}=\mathcal {H}_A\otimes \mathcal {H}_B\) , where \(\mathcal {H}_A\)  encodes the degrees of freedom in the region \(A\)  and \(\mathcal {H}_B\)  the ones in \(B\) .
Given a pure state \(|\psi \rangle \in \mathcal {H}\) , the reduced density matrix of \(A\)  is then given by \(\rho _A\equiv \mathrm {tr}_B|\psi \rangle \langle \psi |\) , where \(\mathrm {tr}_B\)  is the trace over the Hilbert space \(\mathcal {H}_B\) . The Rényi entropies, defined as
\(S_n=\frac{1}{1-n}\ln \mathrm {tr}\rho ^n_A,\) 
